Searching for infrastructure of the quantum mechanical system, we study trajectories of the s-wave poles of the S-matrix element with respect to a real phase $α$ in the complex momentum plane for a complex extension of real potentials by a phase factor $e^{iα}$. This complex extension relates the pole spectrum of the physical system with a potential to the spectrum of another system with the potential of the same shape but of opposite sign. There appear trajectories with the periodicity of $2π$, $4π$, and $\infty$. The appearance of non-recurrent behavior of the trajectory for the change of phase $Δα=2π$ is clearly related with the existence of resonance poles for real repulsive potentials. Dynamical changes of trajectory structure are examined.
Initial momenta of de Broglie-Bohm trajectories generally do not obey quantum mechanical momentum distributions. The solution to this problem presented in the following leads to an extended hydrodynamic interpretation of quantum mechanics. To demonstrate the new formalism, it is applied to the double-slit experiment. From this example follows a proposal for experimental verification of trajectory formulations of quantum mechanics.
Probing Stringy Horizons with Pole-Skipping in Non-Maximal Chaotic Systems
Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences（中国科学院大学 Kavli理论科学研究院）；MIT Center for Theoretical Physics—a Leinweber Institute, Massachusetts Institute of Technology（麻省理工学院莱因韦伯理论物理中心）
For a quantum oscillator with the polynomial potential an explicit expression that describes the energy distribution as a coordinate (and momentum) function is obtained. The presence of the energy function poles is shown for the quantum system in the domains where the Wigner function has negative values.
Weak Values of Momentum of the Electromagnetic Field: Average Momentum Flow Lines, Not Photon Trajectories
在最近的一篇论文中，马勒{ \em et al.}已经论证了Kocsis { \em et al.}的实验为玻姆力学提供了实验依据。不幸的是，这些实验使用相对论性的零静止质量光子，而玻姆力学是基于非相对论性的薛定谔粒子具有非零静止质量。实验结果可以用一种不同的方法来解释，这种方法基于玻姆在他1952年论文的第二篇附录中已经概述过的电磁场。玻姆、希利、霍兰德、卡洛耶鲁、拉姆和杜德尼对这种方法的后续发展，详细地展示了这种理论如何解释一般的实验量子现象。利用这一理论，我们得出这样的结论：实验通过测量我们称之为弱坡印廷矢量的实部来构造平均动量流线。这些结果支持并阐明了Bliokh { \em et al}的分析。实验流线可以独立于光束中的光子数来构建，从而得出结论，流线不能被解释为“光子计数器”。我们讨论了如何在弱值的光场方法中产生光子的概念。
State-to-state reactive integral cross sections (ICS) are often affected by quantum mechanical resonances, especially at relatively low energies. An ICS is usually obtained by summing partial waves at a given value of energy. For this reason, the knowledge of pole positions and residues in the complex energy plane is not sufficient for a quantitative description of the patterns produced by a resonance. Such description is available in terms of the poles of an S-matrix element in the complex plane of the total angular momentum. The approach was recently implemented in a computer code ICS_Regge,…
This is the third (and the last) code in a collection of three programs [Sokolovski et al (2011), Akhmatskaya et al (2014)] dedicated to the analysis of numerical data, obtained in an accurate simulation of an atom-diatom chemical reaction. Our purpose is to provide a detailed description of a FORTRAN code for complex angular momentum (CAM) analysis of the resonance effects in reactive angular scattering [for CAM analysis of integral reactive cross sections see [Akhmatskaya et al (2014)]. The code evaluates the contributions of a Regge trajectory (or trajectories) to a differential cross secti…
The complex eigenvalues of some non-Hermitian Hamiltonians, e.g. parity-time symmetric Hamiltonians, come in complex-conjugate pairs. We show that for non-Hermitian scattering Hamiltonians (of a structureless particle in one dimension) possesing one of four certain symmetries, the poles of the $S$-matrix eigenvalues in the complex momentum plane are symmetric about the imaginary axis, i.e. they are complex-conjugate pairs in complex-energy plane. This applies even to states which are not bounded eigenstates of the system, i.e. antibound or virtual states, resonances, and antiresonances. The fo…
We provide support for the claim that momentum is conserved for individual events in the electron double slit experiment. The natural consequence is that a physical mechanism is responsible for this momentum exchange, but that even if the fundamental mechanism is known for electron crystal diffraction and the Kapitza-Dirac effect, it is unknown for electron diffraction from nano-fabricated double slits. Work towards a proposed explanation in terms of particle trajectories affected by a vacuum field is discussed. The contentious use of trajectories is discussed within the context of oil droplet…
We consider a spin-balanced degenerate gas of spin-1/2 fermions whose dynamics is governed by low-energy $P$-wave interactions, characterized by the scattering volume $a_1$ and effective momentum $r_1$. The energy per particle $\bar{\cal{E}}$ in the many-body system is calculated by resumming the ladder diagrams comprising both particle-particle and hole-hole intermediate states, following the novel advances recently developed by us in Ann.Phys. 437,168741(2022). This allows to obtain a renormalized result for $\bar{\cal{E}}$ within generic cutoff regularization schemes, with $\bar{\cal{E}}$ d…
